Free 2 Asset Portfolio Calculator - Given a portfolio with 2 assets, this determines the expected return (mean), variance, and volatility (standard deviation) of the portfolio.

Free 401(k) Balance Calculator - Determines your 401(k) balance given a salary history per year, contribution percentage rate, employer match percentage, and a rate of return.

A bag contains 7 red, 9 white, and 4 blue marbles. Find the probability of picking 3 blue marbles if each marble is NOT returned to the bag before the next marble is picked. The problem states we will have no replacement. [LIST] [*]First draw probability is 4 blue marbles out of (7 red + 9 white + 4 blue) = 20 marbles (4/20) [*]Second draw probability is 3 blue marbles out of (7 red + 9 white + 3 blue) = 19 marbles (3/19) [*]Third draw probability is 2 blue marbles out of (7 red + 9 white + 2 blue) = 18 marbles (2/18) [/LIST] Each draw is independent, so we multiply the three draws together: 4/20 * 3/19 * 2/18 24/6840 [B]0.0035[/B]

A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. The ball continues to bounce half the height of the previous bounce each time. How far will the ball have traveled when it hits the ground for the fifth time? Take the top of the bounces one at a time: [LIST=1] [*]Ball is dropped 12 feet and it bounces up to 6 feet [*]Ball drops 6 feet back down and bounces up to 3 feet up [*]Ball drops 3 feet back down and bounces up to 1.5 feet up [*]Ball drops 1.5 feet down and bounces up to 0.75 feet up [*]Return down after Bounce 5 is 0.75 feet down [/LIST] [U]Total distance travelled:[/U] 12 + 6 + 6 + 3 + 3 + 1.5 + 1.5 + 0.75 + 0.75 [B]34.5 feet [MEDIA=youtube]OvDp4Y3vOPY[/MEDIA][/B]

A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you draw out a pencil and then draw out a second pencil without returning the first pencil. What is the probability that the first pencil and the second pencil are both green? We are drawing without replacement. Take each draw probability: [LIST=1] [*]First draw, we have a total of 10 + 7 + 8 = 25 pencils to choose from. P(Green) = 8/25 [*]Next draw, we only have 24 total pencils, and 7 green pencils since we do not replace. Therefore, we have P(Green)= 7/24 [/LIST] Since both events are independent, we have: P(Green) * P(Green) = 8/25 * 7/24 P(Green) * P(Green) = 56/600 Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=56&num2=600&num3=&pl=GCF']GCF Calculator[/URL], we see the greatest common factor of 56 and 600 is 8. So we divide top and bottom of the fraction by 8. [B]P(Green) * P(Green) = 7/75[/B]

A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84. What was the rental cost per hour? 9am to 4pm is 7 hours. Cost per hour = Total Cost / Hours Cost per hour = 28.84 / 7 Cost per hour = [B]$4.12[/B]

Free Accounting Rate of Return Calculator - Given an initial investment and a set of returns, this calculates the Accounting Rate of Return

An executive invests $21,000, some at 8% and the rest at 7% annual interest. If he receives an annual return of $1,600, how much is invested at each rate? Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=21000&i1=8&i2=7&itot=1600&pl=Calculate']split fund calculator[/URL], we get: [LIST] [*][B]Fund 1 = 13,000[/B] [*][B]Fund 2 = 8,000[/B] [/LIST]

An executive invests $22,000, some at 7% and the rest at 6% annual interest. If he receives an annual return of $1,420, how much is invested at each rate Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=22000&i1=7&i2=6&itot=1420&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]10,000[/B] @ 7% [*][B]12,000[/B] @ 6% [/LIST]

An executive invests $23,000, some at 8% and some at 4% annual interest. If he receives an annual return of $1,560, how much is invested at each rate? Let x be the amount invested at 8% and y be the amount invested at 4%. We have two equations: [LIST=1] [*]x + y = 23,000 [*]0.08x + 0.04y = 1,560 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+23000&term2=0.08x+%2B+0.04y+%3D+1560&pl=Cramers+Method']system of equations calculator[/URL], we get: [B]x = 16,000 y = 7,000[/B]

An executive invests $29,000, some at 8% and the rest at 6% annual interest. If he receives an annual return of $2,020, how much is invested at each rate? Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=29000&i1=8&i2=6&itot=2020&pl=Calculate']split fund calculator[/URL], we get: [LIST] [*]Fund 1: $14,000 [*]Fund 2: $15,000 [/LIST]

Assuming a standard 52-card deck, what's the probability of dealing three eights in a row when the cards are returned and the deck is shuffled between each draw? There are four (8's) in a standard 52 card deck. The probability of drawing an 8 is: 4/52 [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F52&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we get: 1/13 Now, with each draw, we replace the deck. So each draw of an 8 has a 1/13 probability. And since each of the three draws is independent, we multiply each probability: 1/13 * 1/13 * 1/13 = [B]1/2197 or 0.00045516613[/B]

Beth made a trip to the train station and back. On the trip there she traveled 45 km/h and on the return trip she went 30 km/h. How long did the trip there take if the return trip took six hours? We use the distance formula: D = rt where D = distance, r = rate, and t = time. Start with the return trip: D = 45(6) D = 270 The initial trip is: 270= 30t Divide each side by 30 [B]t = 9 hours[/B]

In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event?

Let me post the whole equation paragraph: Brainteaser # 1: Answer for ACH A fellow geocacher decided that he would try to sell some hand-made walking sticks at the local geocaching picnic event. In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Make sure to multiply and reverse the digits. What would the answer be?

Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge of 76 cents for each mile driven. Hans had to pay 152.99 when he returned the truck. For how many miles did he drive the truck? Set up the equation where x is the amount of miles he drove: 0.76x + 16.95 = 152.99 [URL='http://www.mathcelebrity.com/1unk.php?num=0.76x%2B16.95%3D152.99&pl=Solve']Plug this equation into our calculator[/URL]: x = 179 miles

How MUCH Change would be returned from a $50.00 bill for the purchase of 26 stainless Steel 8-in. bolts at the Price Of 79.5 cents each? Calculate the Stainless Steel Bolts Cost: Stainless Steel Bolts Cost = Number of Stainless Steel Bolts * Price per bolt Stainless Steel Bolts Cost = 26 * 0.795 Stainless Steel Bolts Cost = $20.67 Calculate the change: Change = Cash Offered - Stainless Steel Bolts Cost Change = $50 - $20.67 Change = [B]$29.33[/B]

In planning for a particular job, a painter buys $747 worth of materials. When the job is completed, she returns some unused rollers and brushes for a credit of $38. What was the net amount of her bill? Net bill = Purchase - Returns Net bill = 747 - 38 Net bill = [B]709[/B]

Jessie invests $3345 in the stock market. Over the 3 years she has this invested she gets an average return of 7.8%. How much will her investment be worth after the 3 years? 7.8% = 0.078, so we use our compound interest formula to find our balance after 3 years. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=3345&nval=3+&int=7.8&pl=Annually']compound interest balance calculator[/URL], we get: [B]$4,190.37[/B]

Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15 each. He has $105 to spend. Which of the following can be solved to find the number of shirts he can afford? Let s be the number of shirts. Since shoes are a one-time fixed cost, we have: 15s + 57 = 105 We want to solve this equation for s. We [URL='https://www.mathcelebrity.com/1unk.php?num=15s%2B57%3D105&pl=Solve']type it in our math engine[/URL] and we get: s = [B]3.2 or 3 whole shirts[/B]

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 8 times. Show all work. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. a) What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? b) Find the probability that that she returns at least 1 of the 8 serves from her opponent. (c) How many serves can she expect to return? a) [B]n = 8 p = 0.2[/B] q = 1 - p q = 1 - 0.2 [B]q = 0.8 [/B] b) [B]0.4967[/B] on our [URL='http://www.mathcelebrity.com/binomial.php?n=+8&p=0.2&k=1&t=+5&pl=P%28X+>+k%29']binomial calculator[/URL] c) np = 8(0.2) = 1.6 ~ [B]2[/B] using the link above

Free Modified Internal Rate of Return (MIRR) Calculator - Given a set of positive/negative cash flows, a finance rate, and a reinvestment rate, this calculates the modified internal rate of return

Natalie made a deal with a farmer. She agreed to work for an entire year and in return, the farmer would give her $10,200 plus a prize pig. After working for 5 months, Natalie decided to quit. The farmer determined that 5 months of work was equal to $3375 plus the pig. How much money was the pig worth? The value of a year's work is $10,200 plus a pig of unknown value. The farmer took away $6825 because Natalie worked 5 months. If Natalie worked 7 more months, she would have been paid the additional $6825. 6825/7 months work = $975 per month A full year's work is $975 * 12 = $11,700 Pig value = Full years work - payout Pig value = 11,700 - 10,200 Pig value = [B]1,500[/B]

Free Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index Calculator - Given a series of cash flows C_t at times t and a discount rate of (i), the calculator will determine the Net Present Value (NPV) at time 0, also known as the discounted cash flow model.
Profitability Index
Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Free Portfolio Rate of Return Calculator - Given a portfolio of individual assets with returns and weights, this calculates the total portfolio rate of return.

Free Rates of Return Calculator - Given a set of stock prices and dividends if applicable, this calculates the periodic rate of return and the logarithmic rate of return

Free Roulette Calculator - Calculates the probability for different bets on a roulette wheel including expected return on a monetary bet.

Free Roulette Cumulative Betting Calculator - This calculator displays the probability and return grid for a roulette scenario where you play x games, betting y per number playing z numbers per game.

Free Security Market Line and Treynor Ratio Calculator - Solves for any of the 4 items in the Security Market Line equation, Risk free rate, market return, Β, and expected return as well as calculate the Treynor Ratio.

Free Sharpe Ratio Calculator - Calculates the Sharpe ratio given return on assets, risk free rate, and standard deviation

Free Synthetic Division Calculator - Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable. Also known as the Rational Zero Theorem

Free Volatility Calculator - Given a set of stock prices, this determines expected rates of return and volatility

Free Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM) Calculator - Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.